The importance of group theory was emphasized very recently when some physicists using group theory predicted the existence of a particle that had never been observed before, and described the properties it should have. Later experiments proved that this particle really exists and has those properties.
As for everything else, so for a mathematical theory: beauty can be perceived but not explained.
The differential equations of the propagation of heat express the most general conditions, and reduce the physical questions to problems of pure analysis, and this is the proper object of theory.\r\n
SOURCE: Analytical Theory of Heat
Mathematics is the queen of the sciences, and number theory the queen of mathematics.
The further a mathematical theory is developed, the more harmoniously and uniformly does its construction proceed, and unsuspected relations are disclosed between hitherto separated branches of the science.
A dictionary definition of chaos is a ‘disordered state or collection; a confused mixture.’ This is an accurate description of dynamical systems theory today—or of any other lively field of research.
Number theorists are like lotus-eaters—having once tasted of this food they can never give it up.
Nowadays, group theoretical methods—expecially those involving characters and representations, pervade all branches of quantum mechanics.
The theory of groups is a branch of mathematics in which one does something to something and then compares the results with the result of doing the same thing to something else, or something else to the same thing.
The universe is an enormous direct product of representations of symmetry groups.